Canonical decomposition of even higher order cumulant arrays for blind underdetermined mixture identification

A new family of methods, named 2q-ORBIT (q > 1), is proposed in this paper in order to blindly identify potentially underdetermined mixtures of statistically independent sources. These methods are based on the canonical decomposition of q-th order (q ges 2) cumulants. The latter decomposition is brought back to the decomposition of a third order array whose one loading matrix is unitary. Such a decomposition is then computed by alterning and repeating two schemes until convergence: the first one consists in solving a Procrustes problem while the second one needs to compute the best rank-1 approximation of several q-th order arrays. Computer results show a good efficiency of the proposed methods with respect to classical cumulant-based algorithms especially in the underdetermined case.